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Poster
STEM: A Stochastic Two-Sided Momentum Algorithm Achieving Near-Optimal Sample and Communication Complexities for Federated Learning
Prashant Khanduri · PRANAY SHARMA · Haibo Yang · Mingyi Hong · Jia Liu · Ketan Rajawat · Pramod Varshney

Thu Dec 09 04:30 PM -- 06:00 PM (PST) @
Federated Learning (FL) refers to the paradigm where multiple worker nodes (WNs) build a joint model by using local data. Despite extensive research, for a generic non-convex FL problem, it is not clear, how to choose the WNs' and the server's update directions, the minibatch sizes, and the local update frequency, so that the WNs use the minimum number of samples and communication rounds to achieve the desired solution. This work addresses the above question and considers a class of stochastic algorithms where the WNs perform a few local updates before communication. We show that when both the WN's and the server's directions are chosen based on certain stochastic momentum estimator, the algorithm requires $\tilde{\mathcal{O}}(\epsilon^{-3/2})$ samples and $\tilde{\mathcal{O}}(\epsilon^{-1})$ communication rounds to compute an $\epsilon$-stationary solution. To the best of our knowledge, this is the first FL algorithm that achieves such {\it near-optimal} sample and communication complexities simultaneously. Further, we show that there is a trade-off curve between local update frequencies and local minibatch sizes, on which the above sample and communication complexities can be maintained. {Finally, we show that for the classical FedAvg (a.k.a. Local SGD, which is a momentum-less special case of the STEM), a similar trade-off curve exists, albeit with worse sample and communication complexities. Our insights on this trade-off provides guidelines for choosing the four important design elements for FL algorithms, the update frequency, directions, and minibatch sizes to achieve the best performance.}

#### Author Information

##### Jia Liu (The Ohio State University)

Jia (Kevin) Liu is an Assistant Professor in the Dept. of Electrical and Computer Engineering at The Ohio State University and an Amazon Visiting Academics (AVA). He received his Ph.D. degree from the Dept. of Electrical and Computer Engineering at Virginia Tech in 2010. From Aug. 2017 to Aug. 2020, he was an Assistant Professor in the Dept. of Computer Science at Iowa State University. His research areas include theoretical machine learning, stochastic network optimization and control, and performance analysis for data analytics infrastructure and cyber-physical systems. Dr. Liu is a senior member of IEEE and a member of ACM. He has received numerous awards at top venues, including IEEE INFOCOM'19 Best Paper Award, IEEE INFOCOM'16 Best Paper Award, IEEE INFOCOM'13 Best Paper Runner-up Award, IEEE INFOCOM'11 Best Paper Runner-up Award, IEEE ICC'08 Best Paper Award, and honors of long/spotlight presentations at ICML, NeurIPS, and ICLR. He is an NSF CAREER Award recipient in 2020 and a winner of the Google Faculty Research Award in 2020. He received the LAS Award for Early Achievement in Research at Iowa State University in 2020, and the Bell Labs President Gold Award. His research is supported by NSF, AFOSR, AFRL, and ONR.